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Full Idea
Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers.
Gist of Idea
A sentence is satisfied when we can assert the sentence when the variables are assigned
Source
Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405)
Book Ref
Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], p.405
A Reaction
Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration.
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| 19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten] |